Question

The planet XYZ travels about the star ABC in an orbit that is almost circular. Assume that the orbit is a circle with radius 83,000,000mi. Assume there are 24 hours in one day on planet XYZ.

(a) Assume that XYZ planet year is 366 days, and find the angle formed by XYZ's movement in one day.
(b) Give the angular speed in radians per hour.
(c) Find the linear speed of XYZ in miles per hour.

Answer 1

The angle formed by XYZ's movement in one day is approximately 0.411 radians. The angular speed in radians per hour is approximately 0.0171. The linear speed of XYZ is approximately 1,418,300 mi/hr.

Step-by-step explanation:

(a) To find the angle formed by XYZ's movement in one day, we need to use the formula for circumference of a circle. The formula is given by 2πr, where r is the radius of the circle.

In this case, the radius is 83,000,000 mi, and we know that there are 24 hours in one day on planet XYZ.

So, the angle formed by XYZ's movement in one day is 24/366 multiplied by 2π, which is approximately 0.411 radians.

(b) The angular speed in radians per hour can be found by dividing the angle formed in one day (0.411 radians) by 24 hours. This gives us an angular speed of approximately 0.0171 radians per hour.

(c) The linear speed of XYZ can be found using the formula v = rω, where v is the linear speed, r is the radius of the orbit, and ω is the angular speed.

Substituting the values, the linear speed of XYZ is approximately (83,000,000 mi) * (0.0171 radians per hour) = 1,418,300 mi/hr.